A385534 Decimal expansion of the volume of a biaugmented pentagonal prism with unit edge.

2, 1, 9, 1, 8, 8, 1, 9, 2, 1, 3, 7, 9, 9, 9, 8, 6, 0, 5, 6, 9, 2, 9, 0, 8, 2, 1, 8, 7, 9, 1, 8, 4, 2, 2, 9, 2, 2, 6, 3, 9, 3, 1, 4, 6, 1, 8, 0, 2, 5, 1, 4, 3, 5, 3, 5, 9, 9, 3, 2, 1, 2, 8, 6, 3, 5, 4, 1, 1, 3, 1, 5, 1, 6, 9, 6, 3, 3, 5, 2, 4, 4, 2, 8, 2, 5, 7, 0, 4, 1

Offset

1,1

Comments

The biaugmented pentagonal prism is Johnson solid J_53.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Wikipedia, Biaugmented pentagonal prism.

Index entries for algebraic numbers, degree 8.

Formula

Equals sqrt(257 + 90*sqrt(5) + 24*sqrt(50 + 20*sqrt(5)))/12 = sqrt(257 + 90*A002163 + 24*sqrt(50 + 20*A002163))/12.

Equals the largest root of 429981696*x^8 - 3069591552*x^6 + 5343542784*x^4 - 2504731968*x^2 + 10569001.

Example

2.1918819213799986056929082187918422922639314618025...

Mathematica

First[RealDigits[Sqrt[257 + 90*Sqrt[5] + 24*Sqrt[50 + 20*Sqrt[5]]]/12, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J53", "Volume"], 10, 100]]

Crossrefs

Cf. A385535 (surface area).

Cf. A002163, A385509.

Sequence in context: A187549 A261124 A100945 * A133399 A128751 A129168

Adjacent sequences: A385531 A385532 A385533 * A385535 A385536 A385537

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jul 03 2025

Status

approved